Math Question and Answers


Question and Answers Forum

All Questions Topic List
Algebra Questions
Previous in All Question Next in All Question
Previous in Algebra Next in Algebra
Question Number 172264 by Mikenice last updated on 25/Jun/22

	Answered by Rasheed.Sindhi last updated on 25/Jun/22
	$log_2 (log_8 x)=log_8 (log_2 x) log_2 (((log_2 x )/(log_2 8 )))=((log_2 (log_2 x) )/(log_2 8)) log_2 (((log_2 x )/(3 )))=((log_2 (log_2 x) )/3) 3{log_2 (log_2 x)−log_2 3}=log_2 (log_2 x) log_2 x=y 3log_2 y−3log_2 3=log_2 y 2log_2 y−3log_2 3=0 log_2 y^2 =log_2 3^3 y^2 =3^3 (log_2 x )^2 =27$
	$\log_{2} (\log_{8} x) = \log_{8} (\log_{2} x)$ $\log_{2} (\frac{\log_{2} x}{\log_{2} 8}) = \frac{\log_{2} (\log_{2} x)}{\log_{2} 8}$ $\log_{2} (\frac{\log_{2} x}{3}) = \frac{\log_{2} (\log_{2} x)}{3}$ $3 {\log_{2} (\log_{2} x) - \log_{2} 3} = \log_{2} (\log_{2} x)$ $\log_{2} x = y$ ${3 \log}_{2} y - {3 \log}_{2} 3 = \log_{2} y$ ${2 \log}_{2} y - {3 \log}_{2} 3 = 0$ $\log_{2} y^{2} = \log_{2} 3^{3}$ $y^{2} = 3^{3}$ ${(\log_{2} x)}^{2} = 27$
	Commented by Tawa11 last updated on 25/Jun/22

	$Great sir$
	Commented by Rasheed.Sindhi last updated on 25/Jun/22

	$T han k s miss!$
	Answered by greougoury555 last updated on 25/Jun/22
	$let log _8 x = u⇒log _2 x = 3u ⇒ log _2 (u)=log _8 (3u) ⇒log _2 (u^3 )=log _2 (3u) ⇒u^3 −3u=0 ⇒u(u^2 −3)=0 ⇒ { ((u=0⇒x=1)),(((log _8 x)^2 =3⇒(log_2 x)^2 = 27 )) :}$
	$l e t \log_{8} x = u \Rightarrow \log_{2} x = 3 u$ $\Rightarrow \log_{2} (u) = \log_{8} (3 u)$ $\Rightarrow \log_{2} (u^{3}) = \log_{2} (3 u)$ $\Rightarrow u^{3} - 3 u = 0 \Rightarrow u (u^{2} - 3) = 0$ $\Rightarrow {\begin{cases} u = 0 \Rightarrow x = 1 \\ {(\log_{8} x)}^{2} = 3 \Rightarrow {(\log_{2} x)}^{2} = 27 \end{cases}$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum